Đáp án:
$\begin{array}{l}
a)\left( {x + 4} \right)\left( {{x^2} - 4x + 16} \right) - x\left( {x - 5} \right)\left( {x + 5} \right) = 264\\
\Leftrightarrow {x^3} + {4^3} - x\left( {{x^2} - 25} \right) = 264\\
\Leftrightarrow {x^3} + 64 - {x^3} + 25x = 264\\
\Leftrightarrow 25x = 200\\
\Leftrightarrow x = 8\\
Vậy\,x = 8\\
b){\left( {x - 2} \right)^3} - \left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right) + 6\left( {x - 2} \right)\left( {x + 2} \right) = 0\\
\Leftrightarrow {x^3} - 6{x^2} + 12x - 8 - {x^3} + 8 + 6\left( {{x^2} - 4} \right) = 0\\
\Leftrightarrow - 6{x^2} + 12x + 6{x^2} - 24 = 0\\
\Leftrightarrow 12x = 24\\
\Leftrightarrow x = 2\\
Vậy\,x = 2\\
c){\left( {x - 1} \right)^3} - \left( {{x^2} - 3x + 9} \right)\left( {x + 3} \right) + 3\left( {x - 2} \right)\left( {x + 2} \right) = 2\\
\Leftrightarrow {x^3} - 3{x^2} + 3x - 1 - \left( {{x^3} + {3^3}} \right) + 3\left( {{x^2} - 4} \right) = 2\\
\Leftrightarrow {x^3} - 3{x^2} + 3x - 1 - {x^3} - 27 + 3{x^2} - 12 = 2\\
\Leftrightarrow 3x = 42\\
\Leftrightarrow x = 14\\
Vậy\,x = 14\\
d){\left( {2x - 1} \right)^2} + {\left( {x + 3} \right)^2} - 5\left( {x - 7} \right)\left( {x + 7} \right) = 0\\
\Leftrightarrow 4{x^2} - 4x + 1 + {x^2} + 6x + 9 - 5\left( {{x^2} - 49} \right) = 0\\
\Leftrightarrow 5{x^2} + 2x + 10 - 5{x^2} + 245 = 0\\
\Leftrightarrow 2x = - 255\\
\Leftrightarrow x = - 127,5\\
Vậy\,x = - 127,5
\end{array}$
